The control is chosen in the whole \(A={\mathbb {R}}^2\)  (despite the fact that for classic results it is possible to prove that the optimal control is always included in a compact subset of \({\mathbb {R}}^2\) , cf. [1]}) and the problem lives in the domain \(\Omega =[-1,1]^2\) . The target set is composed by the points
\( {\mathcal {T}}_j=0.6\,\left(\cos \left(j\frac{2\pi }{3}\right),\sin \left(j\frac{2\pi }{3}\right)\right), \quad j=1,\ldots ,3.\) 
